Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Probability

NDA 2021 · Mathematics · Probability

If P(A B) < P(A) , then which one of the following is correct?

If P(A∣B)<P(A)P(A \mid B) < P(A), then which one of the following is correct?

Options

  1. AP(B∣A)<P(B)P(B \mid A) < P(B)
  2. BP(B∣A)>P(B)P(B \mid A) > P(B)
  3. CP(B∣A)=P(B)P(B \mid A)=P(B)
  4. DP(B∣A)>P(A)P(B \mid A) > P(A)

Correct answer

A. P(B∣A)<P(B)P(B \mid A) < P(B)

Step-by-step solution

P(A/B)<P(A)⇒P(A∩B)P(A)<P(A)⇒P(A∩B)<P(A)P(B)⇒P(A∩B)P(A)<PB⇒P(B/A)<P(B)\begin{aligned} & \mathrm{P}(\mathrm{A} / \mathrm{B}) < \mathrm{P}(\mathrm{A}) \Rightarrow \frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} < \mathrm{P}(\mathrm{A}) \\ & \Rightarrow \mathrm{P}(\mathrm{A} \cap \mathrm{B}) < \mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B}) \\ & \Rightarrow \frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})} < \mathrm{PB} \Rightarrow \mathrm{P}(\mathrm{B} / \mathrm{A}) < \mathrm{P}(\mathrm{B})\end{aligned}
Practice Probability on Quantrex Academy →

More from Probability

Passage: Four dice are rolled. Question: What is the probability that getting a total of… NDA 2026Three events A , B and C are such that A and B are disjoint, A and C are independent, B… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026Passage: Four dice are rolled. Question: What is the probability that getting a total of… NDA 2026For a Binomial distribution with mean 6 and standard deviation 2 , what is the value of… NDA 2026Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3… NDA 2026In an entrance test there are multiple choice questions. There are four options for each… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026Consider the following statements in respect of the events A , B , C : I. (A B C) ( A B C… NDA 2026Passage: Let A , B , C and D be mutually exclusive and exhaustive events and… NDA 2026The probability that a family owns a laptop is 0.68 ; that it also owns a desktop is 0.56… NDA 2025An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is… NDA 2025An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is… NDA 2025Under which of the following conditions may binomial distribution be used? I. The number… NDA 2025Three faces of a die are black, two faces are white and one face is red. The die is… NDA 2025A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6… NDA 2025 Full Probability list Probability JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs